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A Study of Photon Trapping and the ac Stark Effect in Photonic Crystals and Dispersive Materials

I. Haque

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

In this thesis, we study light-matter interaction in the contexts of coherent population trapping (CPT) and the ac Stark effect in nanoparticles embedded (doped) in two important classes of reservoirs -- photonic crystals and dispersive materials. These materials have gaps in their energy spectra and are studied widely due to their unusual optical properties and potential for novel applications. We consider that the reservoirs are doped with an ensemble of five-level nanoparticles, each with a single Λ core (consisting of a lower doublet and an upper energy level), which interact with both the host reservoir and external radiation fields. We have also included studies of cases where the nanoparticles interact with each other as well via dipole-dipole interaction (DDI), which is included in the mean field approximation. This only happens when the doping concentration is high (~ 1018 per cubic meter).\nIn studying CPT, we have developed a novel technique of optical switching by devising a system whereby the doped nanoparticles become stable against absorption from the radiation field(s) i.e. they switch to their ground states. We have confirmed the occurrence of CPT in both types of reservoir and have also identified a number of important contrasting features which have markedly different utilities. Most significantly, we have found that the strength of the DDI between the nanoparticles plays a very important role in determining the conditions required for CPT in both materials. In studying the ac Stark effect in photonic crystals, we have used an ensemble of five-level nanoparticles, each with a single cascade core [ladder configuration], both with and without DDI. We found that, in the ac Stark regime, resonance tuning of the transitions within the nanoparticles, in relation to the band structure of these crystals, offers a new mechanism for switching the nanoparticle system from an inverted to a non-inverted state. Specifically, a doped nanoparticle can effectively become transparent to any radiation field tuned to the probed transition. Under DDI, we found that the absorption in the system decreases with increasing DDI strength. These findings have very exciting potential for applications in optical switching.

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In this thesis, we study light-matter interaction in the contexts of coherent population trapping (CPT) and the ac Stark effect in nanoparticles embedded (doped) in two important classes of reservoirs -- photonic crystals and dispersive materials. These materials have gaps in their energy spectra and are studied widely due to their unusual optical properties and potential for novel applications. We consider that the reservoirs are doped with an ensemble of five-level nanoparticles, each with a single Λ core (consisting of a lower doublet and an upper energy level), which interact with both the host reservoir and external radiation fields. We have also included studies of cases where the nanoparticles interact with each other as well via dipole-dipole interaction (DDI), which is included in the mean field approximation. This only happens when the doping concentration is high (~ 1018 per cubic meter).\nIn studying CPT, we have developed a novel technique of optical switching by devising a system whereby the doped nanoparticles become stable against absorption from the radiation field(s) i.e. they switch to their ground states. We have confirmed the occurrence of CPT in both types of reservoir and have also identified a number of important contrasting features which have markedly different utilities. Most significantly, we have found that the strength of the DDI between the nanoparticles plays a very important role in determining the conditions required for CPT in both materials. In studying the ac Stark effect in photonic crystals, we have used an ensemble of five-level nanoparticles, each with a single cascade core [ladder configuration], both with and without DDI. We found that, in the ac Stark regime, resonance tuning of the transitions within the nanoparticles, in relation to the band structure of these crystals, offers a new mechanism for switching the nanoparticle system from an inverted to a non-inverted state. Specifically, a doped nanoparticle can effectively become transparent to any radiation field tuned to the probed transition. Under DDI, we found that the absorption in the system decreases with increasing DDI strength. These findings have very exciting potential for applications in optical switching.
In this paper we present calculations of level populations and susceptibility for an ensemble of five-level atoms doped in a photonic crystal, using the master equation method. The atoms in the ensemble interact with the crystal which acts as a reservoir and are coupled with two strong pump fields and a weak probe field. It is found that, by manipulating the resonance energy associated with one of the decay channels of the atom, the system can be switched between an inverted and a non-inverted state. We have also observed the ac Stark effect in these atoms and have shown that due to the role played by the band structure of the photonic crystal, it is possible to switch between an absorption state and a non-absorption state of the atomic system. This is a very important finding as techniques of rendering material systems transparent to resonant laser radiation are very desirable in the fabrication of novel optical and photonic devices.
A theory of coherent population trapping (CPT) has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials when doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra leading to unusual optical properties. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. The transition between the two lower states of an atom is dipole forbidden. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations are performed for both PBG and DPBG materials with the phase factor between the coherent states chosen such that the number density of the upper state becomes zero when the photon fields have the same intensity. It is found that when the resonance energies lie away from the band edges and within the lower band, the CPT effect is observed in both materials when the fields have identical intensities. Similar results are also found when the resonance energies lie away from the band edges and within the upper band. When one of the resonance energies lies near the lower band edge, the number density vanishes at all intensities of the fields for both materials. This is an effect of the band structure of the materials and is not due to the CPT effect. A similar result is seen when one of the resonance energies lies near the upper band edge of a PBG material. However, for a DPBG material, the number density does not become zero when one of the resonance energies lies near the upper band edge, except due to the CPT effect brought on by the identical intensities of the photon fields. This is a very interesting phenomenon.
A theory of nonlinear phenomena has been developed for a photonic crystal in the presence of a pump and a coupling laser field. The crystal is doped with an ensemble of four-level nanoparticle impurities. It is considered that the impurity particles are not only interacting with the photonic crystal but also with each other via dipole-dipole interaction. An expression for the susceptibility has been obtained using the density matrix method. The nonlinear effects due to the coupling and the pump fields have been included in the formulation. The absorption spectrum has been calculated in the presence of the strong coupling and pump fields for an isotropic photonic crystal made from dielectric spheres. The photonic crystal has a gap to midgap ratio of about 21%. It is predicted that the absorption spectrum in the photonic crystal can have zero, one, two or three absorptionless states by tuning one of the transition energies within the bands. This is an interesting phenomenon which can be used to make photonic switching devices. We have also calculated the absorption spectrum in the presence of the dipole-dipole interaction. It is found that a symmetric absorption spectrum changes to an asymmetric one due to this interaction. It is also found that there is a large enhancement in the absorption and the dispersion simultaneously for certain values of the detuning and concentration.
A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Quantum optics of metallic photonic crystals is studied in this paper. Crystals are made from metallic spheres and a background dielectric material. The refractive index of the metallic spheres depends on the frequencies of the incident light and plasmons whereas the refractive index of the background material is a constant. Crystals are lightly doped with four-level nanoparticles. It is considered that nanoparticles are interacting with the metallic crystals via electron-photon interaction in the dipole approximation. The probe and pump laser fields are applied to monitor the absorption spectrum in the system. Two transparent states are predicted. One is due to the electromagnetically induced transparency and the other is due to the electron-photon interaction. For certain experimental conditions these transparent states merge into one transparent state. The effect of plasmon frequencies has also been studied. It is found that the system can be switched from a transparent state to an absorbing state just by changing the frequency of plasmons. This study can be used to makes new types of optical devices such as switches and optical transistors.
A theory of linear susceptibility has been developed in the presence of dipole-dipole interaction for photonic-band-gap (PBG) materials doped with an ensemble of five-level nanoparticles. An external probe laser induces dipole moments in nanoparticles. When the concentration of the particles is high, the induced dipoles interact with one another through dipole-dipole interaction. Mean-field theory is used to include the effect of dipole-dipole interaction in the calculation of susceptibility. Numerical simulations are performed for the real and imaginary susceptibilities and it is found that the system switches between inversionless and noninversionless states. In addition the system switches between absorptionless and nonabsorptionless states. These occur when the resonance energy lies near the valence-band edge of the photonic-band-gap material. The theory also predicts a polarization catastrophe in PBG materials doped with nanoparticles.